6. Trigonometric Identities and More Equations

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). 4 cos² x = 5 - 4 sin x

In Exercises 55–58, use the given information to find the exact value of each of the following:

a. sin(α/2)

tan α = 4/3, 180° < α < 270°

In Exercises 55–58, use the given information to find the exact value of each of the following:

b. cos(α/2)

tan α = 4/3, 180° < α < 270°

In Exercises 55–58, use the given information to find the exact value of each of the following:

c. tan(α/2)

sec α = ﹣3, 𝝅/2 < α < 𝝅

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). cos 2x + 5 cos x + 3 = 0

Solve each equation for all exact solutions, in radians.

cos 2x + cos x = 0

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.

csc² θ ―2 cot θ = 0

In Exercises 55–58, use the given information to find the exact value of each of the following:

a. sin(α/2)

sec α = ﹣3, 𝝅/2 < α < 𝝅

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.

sin² θ ― 2 sin θ + 3 = 0

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). tan x + sec x = 1

Find one solution for each equation. Assume all angles involved are acute angles. cos(3θ + 11°) = sin( 7θ + 40°) 5 10

Solve each equation over the interval [0°, 360°). Write solutions as exact values or to the nearest tenth, as appropriate.

cot θ + 2 csc θ = 3

Solve each equation over the interval [0, 2π). Write solutions as exact values or to four decimal places, as appropriate.

sin x/2 - cos x/2 = 0

Solve each equation (x in radians and θ in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures.

sin θ cos θ ― sin θ = 0

In Exercises 63–84, use an identity to solve each equation on the interval [0, 2𝝅). sin 2x cos x + cos 2x sin x = √ 2/2